Learning Dynamics and the Co-Evolution of Competing Sexual Species

Authors Georgios Piliouras, Leonard J. Schulman



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Georgios Piliouras
Leonard J. Schulman

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Georgios Piliouras and Leonard J. Schulman. Learning Dynamics and the Co-Evolution of Competing Sexual Species. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 59:1-59:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.ITCS.2018.59

Abstract

We analyze a stylized model of co-evolution between any two purely competing species (e.g., host and parasite), both sexually reproducing. Similarly to a recent model [Livnat et al. FOCS'14] the fitness of an individual depends on whether the truth assignments on n variables that reproduce through recombination satisfy a particular Boolean function. Whereas in the original model a satisfying assignment always confers a small evolutionary advantage, in our model the two species are in an evolutionary race with the parasite enjoying the advantage if the value of its Boolean function matches its host, and the host wishing to mismatch its parasite. Surprisingly, this model makes a simple and robust behavioral prediction. The typical system behavior is periodic. These cycles stay bounded away from the boundary and thus, learning-dynamics competition between sexual species can provide an explanation for genetic diversity. This explanation is due solely to the natural selection process. No mutations, environmental changes, etc., need be invoked. The game played at the gene level may have many Nash equilibria with widely diverse fitness levels. Nevertheless, sexual evolution leads to gene coordination that implements an optimal strategy, i.e., an optimal population mixture, at the species level. Namely, the play of the many "selfish genes" implements a time-averaged correlated equilibrium where the average fitness of each species is exactly equal to its value in the two species zero-sum competition. Our analysis combines tools from game theory, dynamical systems and Boolean functions to establish a novel class of conservative dynamical systems.
Keywords
  • Dynamical Systems
  • Potential Game
  • Team Zero-Sum Game
  • Boolean Functions
  • Replicator Dynamics

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References

  1. G. Bell. The Masterpiece Of Nature: The Evolution and Genetics of Sexuality. Univ. of California Press, 1982. Google Scholar
  2. C. W. Benkman, T. L. Parchman, A. Favis, and A. M. Siepielski. Reciprocal selection causes a coevolutionary arms race between crossbills and lodgepole pine. The American Naturalist, 162(2):182-194, 2003. Google Scholar
  3. E. D. Brodie Jr., B. J. Ridenhour, and E. D. Brodie III. The evolutionary response of predators to dangerous prey: Hotspots and coldspots in the geographic mosaic of coevolution between garter snakes and newts. Evolution, 56(10):2067-2082, 10 2002. Google Scholar
  4. E. Chastain, A. Livnat, C. Papadimitriou, and U. Vazirani. Multiplicative updates in coordination games and the theory of evolution. In Proceedings of the 4th Conference on Innovations in Theoretical Computer Science, ITCS '13, pages 57-58, New York, NY, USA, 2013. ACM. Google Scholar
  5. Erick Chastain, Adi Livnat, Christos Papadimitriou, and Umesh Vazirani. Algorithms, games, and evolution. Proceedings of the National Academy of Sciences, 111(29):10620-10623, 2014. Google Scholar
  6. P. R. Ehrlich and P. H. Raven. Butterflies and plants: A study in coevolution. Evolution, 18(4):586-608, Dec. 1964. Google Scholar
  7. M. Eigen. Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften, 58(10):465-523, 1971. Google Scholar
  8. M. Eigen and P. Schuster. The Hypercycle: A Principle of Natural Self-Organization. Springer-Verlag, 1979. Google Scholar
  9. S. Gavrilets. Fitness Landscapes and the Origin of Species. Princeton University Press, 2004. Google Scholar
  10. A. Livnat and C. Papadimitriou. Sex as an algorithm: the theory of evolution under the lens of computation. Communications of the ACM (CACM), 59:84-93, November 2016. Google Scholar
  11. A. Livnat, C. Papadimitriou, A. Rubinstein, A. Wan, and G. Valiant. Satisfiability and evolution. In FOCS, 2014. Google Scholar
  12. R. Mehta, I. Panageas, and G. Piliouras. Natural selection as an inhibitor of genetic diversity. In ITCS, 2015. Google Scholar
  13. R. Mehta, I. Panageas, G. Piliouras, P. Tetali, and V. V. Vazirani. Mutation, sexual reproduction and survival in dynamic environments. In ITCS, 2017. Google Scholar
  14. T. Nagylaki. The evolution of multilocus systems under weak selection. Genetics, 134(2):627-47, 1993. Google Scholar
  15. M. A. Nowak and H. Ohtsuki. Prevolutionary dynamics and the origin of evolution. Proceedings of the National Academy of Sciences, 105(39):14924-14927, 2008. Google Scholar
  16. O. Pellmyr. Yuccas, yucca moths, and coevolution: A review. Annals of the Missouri Botanical Garden, 90(1):35-55, 2003. Google Scholar
  17. G. Piliouras and L. J. Schulman. Learning dynamics and the co-evolution of competing sexual species. Arxiv preprint, 2017. URL: https://arxiv.org/abs/1711.06879.
  18. J. N. Thompson. The Coevolutionary Process. U Chicago Press, 1994. Google Scholar
  19. J. N. Thompson. The Geographic Mosaic of Coevolution. U Chicago Press, 2005. Google Scholar
  20. J. N. Thompson and B. M. Cunningham. Geographic structure and dynamics of coevolutionary selection. Nature, 417:735-738, 2002. URL: http://dx.doi.org/10.1038/nature00810.
  21. L. Van Valen. A new evolutionary law. Evolutionary Theory, 1:1-30, 1973. Google Scholar
  22. L. Valiant. Probably Approximately Correct: Nature’s Algorithms for Learning and Prospering in a Complex World. Basic Books, 2013. Google Scholar
  23. J. W. Weibull. Evolutionary Game Theory. MIT Press; Cambridge, MA, 1995. Google Scholar
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